Problem: Find the slope and y-intercept of the line that is ${\text{parallel}}$ to $\enspace {y = -x - 2}\enspace$ and passes through the point ${(5, 3)}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$
Solution: Parallel lines have the same slope. The slope of the blue line is ${-1}$ , so the equation of our parallel line will be of the form $\enspace {y = -x + b}\enspace$ We can plug our point, $(5, 3)$ , into this equation to solve for ${b}$ , the y-intercept. $3 = {-}(5) + {b}$ $3 = -5 + {b}$ $3 + 5 = {b} = 8$ The equation of the parallel line is $\enspace {y = -x + 8}\enspace$. ${m = -1, \enspace b = 8}$